Recently I became interested in liberal arts colleges. However, starting last year, I picked up the pace in my math education. I tested into my school’s Calc class then taught myself BC and got a 5. Now I’m in Calc 3 and plan on taking Diff Eq and Linear Algebra next semester. Basically what I am wondering is if LACs, specifically Carleton and Williams, would be suitable for the kinds of courses I’d eventually like to take.
Look online at the course offerings in the math department at these schools and see if they are what you want.
You’ll be right at home in the Williams math dept.
You don’t say what year you are in high school but I’m going to assume you’re a junior who’s going to be done with multivariable calculus, differential equations and linear algebra at the end of your junior year and possibly some higher level math next year, your senior year.
At Carleton, not counting special topics courses, independent study/project courses, and the education-related ones, it seems like there are 25 upper-division math and statistics courses you can take beyond the calculus sequence and ODE. Of course not all of them will be offered every year. If you have to take ~12-15 courses to round out a major, that’d be nearly half the department’s courses. That’s plenty of classes, but the question is will the different classes be offered consistently enough for you to have some variety and choice. I’d check out not just the overall catalog but the course registration online to see what the pattern has been in past semesters. You’ll probably be all right, but it’s good to check.
When I went to count the Williams classes (excluding the classes you already took, anything below the 200-level, and independent studies) I counted up to around 40 before I got tired of counting. I was near but not at the end of the list…and I hadn’t gotten to the statistics courses yet. You’ll certainly be fine at Williams, as @marvin100 has already pointed out.
And if you are interested in liberal arts colleges and math, check out Harvey Mudd! Also check out LACs that are in consortia with larger universities, like Swarthmore and Haverford, or Amherst. Or there’s the option of attending an LAC that’s physically nearby a university with graduate math departments, like Occidental is about 20 minutes from USC and about 35 minutes from UCLA.
If you will complete college sophomore level math as a high school junior, you are likely to want to take graduate level math courses as an undergraduate and do graduate-level research as an undergraduate, if you major in math. LACs generally offer only undergraduate level courses, although Harvey Mudd does offer some graduate level math courses, and some math courses at Williams appear to include topics usually covered in graduate level math courses.
Be sure to check how frequently each course of interest is offered. That may actually be less of a problem for you than for many other students, since you have a three or four year window to catch each junior or senior level course of interest, as opposed to a two year window that most students have due to needing to complete frosh and soph level prerequisites before being able to take junior and senior level courses.
Note that even at the biggest universities, junior/senior (and graduate) level math courses tend to be small, so the small class size advantage of a LAC will be less for you in your math major than it is for many other students. You would gain a small class size advantage if you take introductory courses in other subjects, though.
Take a look at St. Olaf. Strong math dept.
I would look at muhlenberg college…
http://www.muhlenberg.edu/main/academics/mathcs/math-courses.html#mth227
those classes should keep you plenty busy and prepare you for graduate school!
Some LACs not yet mentioned that are strong in math include Grinnell, Hamilton, Bowdoin, Haverford and Reed. However, with your level of advancement, a semester or year in Budapest (generally available) may be advisable – should you choose an LAC – if you are to progress in mathematics through your four years as an undergraduate. Faculty guided research would also likely be part of your education.
That lists only 16 junior/senior level math courses, including statistics. None look like they cover graduate level topics. Many seem to be applied math courses that would not be the emphasis of someone preparing for PhD study in math.
Williams, Carleton, Grinnell, St. Olaf, Haverford and Harvey Mudd will all offer you all you could ask for in an undergraduate Math education in an LAC environment.
Good luck!
A look at the course catalogs and schedules indicates that Williams and Harvey Mudd are more suitable than the others for a student in the OP’s situation. Grinnell and Haverford appear to be the most limited for a student in the OP’s situation.
Haverford or Swarthmore may work if the OP is willing to take the train to Penn. For that, the train from Swarthmore puts the student a couple of short blocks away from the Penn math department. Williams would be a better choice.
Check out colleges who participate in the Budapest Math program, too - one semester or year doing advanced math.
Overall, you should be fine at the two LACs you cited, and looking into colleges in consortia would also be very appropriate, or with access to graduate programs.
You’d be pretty “normal” for HarveyMudd. 
@ucbalumnus Agree on the Muhlenberg math now that you’ve drawn my attention to it. The OP wouldn’t be interested in a bunch of them and would exhaust the rest quickly. Curious what you think about their Physics offerings, which I’m in less of a position to judge, but don’t want to thread hijack
Union College, Lafayette and Bucknell might be worth a look. These schools have very good engineering programs.
What classes you want to take may not be compatible with what is required for a degree. The same general subject matter in college may be dramatically more difficult than high school.
The idea you will overrun the Math department at a good school is probably not going to happen.
A good engineering program does not necessarily mean that the math department has sufficient advanced offerings for a math major as advanced as the OP.
It could easily happen to the OP at Union College. http://www.math.union.edu/courses/descriptions/all-courses.html lists its math offerings. There are only 9 junior/senior level (300/400 level) math courses listed.
Bucknell has 16 junior/senior level math courses listed at http://coursecatalog.bucknell.edu/collegeofartsandsciencescurricula/areasofstudy/mathematicsmath/#courseinventory , but that includes 4 courses in statistics.
An accomplished math professor from a public university told me that, in his opinion, Macalester College is probably the best liberal arts college in the Midwest (and one of the best in the country) for math majors. That’s just one opinion and it surprised me. I knew Macalester was very well regarded, but I didn’t realize it was THAT well regarded. He said he was basing his opinion on faculty he knew, not on profiles of entering students. He acknowledged that Grinnell and Carleton probably accepted, on average, high school seniors with higher scores on their math SATs and ACTs. But he still thought Macalester was better. One other plus for Macalester is that it is very close to the University of Minnesota.
check out Holy Cross.
Macalester was recognized in a Princeton Review subcategory, “Great Schools for Mathematics Majors.” Of the 26 schools, 16 are LACs:
Agnes Scott
Bowdoin
Bryn Mawr
Carleton
College of the Holy Cross
The College of Idaho
Grinnell
Hamilton
Harvey Mudd
Haverford
Macalester
Randolph
Reed
St. Lawrence
St. Olaf
Wabash
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However, the OP should carefully check the offerings of each school. What may be a good school for a math major who is not advanced or only up to a year advanced (single variable calculus in high school) may leave a highly advanced math student like the OP running out of courses to take. In addition to the number of junior/senior level math courses offered, the OP should also consider whether any include graduate-level material.